Re: What else
Once a crime is reported Police have to resolve - by caution, restorative justice or referral to CPS. There is almost no option for the officer to go "don't be silly".
I suspect your statement is somewhat incorrect. The police are there to investigate reported crimes, and determine if there is any grounds for prosecution. They do have the ability to decide that no crime was committed (eg find someone breaking into a car, turns out to be the car's owner who'd locked keys inside). Even if the officers themselves cannot decide not to proceed, those above them have that discretion and if they're presented with enough evidence of innocence or a lack of evidence of guilt (such that a trial is very likely to be lost) they don't proceed with a prosecution. The only time a prosecution goes ahead is when there is a personal vendetta involved, or utter stupidity on the part of those who decide to prosecute (sometimes both).
Besides, the article reads like it was said copper who "discovered" the picture (strangely just one out of hundreds) and took it upon himself to prosecute further.
And as your so-called "Reg commentards" have pointed out, if the police really did have concerns that there was a threat or gun offence here, why did they not search the guys house? The answer is probably quite obvious - they didn't search because they already knew he was innocent.